Aquatic Chemistry - American Chemical Society

---

12 The Chemical Effects of Collapsing Cavitation Bubbles Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

Mathematical Modeling Anatassia Kotronarou and Michael R. Hoffmann* W. M . Keck Laboratories, California Institute of Technology, Pasadena, C A 91125

A comprehensive mechanism is developed for aqueous-phase oxidation of S(-II), where [S(-II)] = [H S] + [HS ] 2

+ [S ], by OΗ radical in

-

2-

•

the presence of oxygen. The oxidation of S(-II) is initiated by reaction with OH, but it is further propagated by a free-radical chain sequence •

involving O . This mechanism can adequately model the observed oxi­ 2

dation of S(-II) in air-saturated aqueous solutions sonicated at 20 kHz and 75 W/cm

2

at pH

≥10, assuming a continuous and uniform OH •

input into solution from the imploding cavitation bubbles. At this pH range, practically all S(-II) is present in the form of HS and cannot -

undergo thermal decomposition. Our work suggests that the use of simplified approaches for modeling the liquid-phase sonochemistry of a well-mixed solution may be justified when OΗ radical reactions pre­ •

dominate. For the immersion probe at 20 kHz and 75 W/cm , 2

the

effective OΗ uniform release into the bulk solution was estimated to •

be 3.5 μΜ/min of

THE

with a corresponding steady-state OH concentration •

≤0.1 μΜ.

A C T I O N O F U L T R A S O N I C WAVES I N L I Q U I D S can induce or accelerate a

wide variety of chemical reactions (1, 2) The chemical effects of ultrasound have been explained in terms of reactions occurring inside, at the interface, or at some distance away from cavitating gas bubbles. In the interior of a collapsing cavitation bubble, extreme but transient conditions exist. Temper*Corresponding author

0065-2393/95/0244-0233$08.00/0 © 1995 American Chemical Society

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

234

AQUATIC CHEMISTRY

atures approaching 5000 Κ have been determined, and pressures of several hundred atmospheres have been calculated. Temperatures on the order of 2000 Κ have been determined for the interfacial region surrounding a col­ lapsing bubble. Sonochemical reactions are characterized by the simultaneous occurrence of pyrolysis and radical reactions, especially at high solute concentrations. Vol­ atile solutes will undergo direct pyrolysis reactions within the gas phase of the collapsing bubbles or within the hot interfacial region. In these interfacial regions, both combustion and free-radical reactions (e.g., involving Ό Η de­ rived from the decomposition of H 0 ) are possible. Pyrolysis (i.e., combustion) in the interfacial region is predominant at high solute concentrations, whereas at low solute concentrations free-radical reactions are likely to predominate. In the bulk solution, the chemical reaction pathways are similar to those ob­ served in aqueous radiation chemistry [as induced by aquated electrons (e -), gamma rays (7), or X-rays]. However, combustion-like reactions may occur at low solute concentrations with nonvolatile surfactants and polymers. The chemical effects of ultrasonic irradiation are a direct result of acoustic cavitation. Sound waves traveling through water with frequencies greater than 15 k H z force the growth and subsequent collapse of small bubbles of gas in response to the passage of expansion and compression waves. The greatest coupling occurs when the natural resonance frequency of the bubble equals the ultrasonic frequency (e.g., 20 k H z = a bubble diameter of 130 μηι). The chemical effects are realized during and immediately after collapse of a vaporfilled cavitation bubble. During bubble collapse, which occurs within 100 ns, H 0 undergoes thermal dissociation to give H ' atoms and Ό Η radicals.

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

2

2

H 0 2

u>15kHz

• Η* + Ό Η

,

v

(1)

We are motivated, in part, by the potential economical application of electrohydraulic cavitation for the rapid degradation of a wide range of chem­ ical contaminants. Current approaches to the treatment of hazardous chemical wastes include high-temperature incineration; chemical oxidation with 0 , H 0 , and U V light; membrane separation; activated carbon adsorption; sub­ strate-specific biodégradation; electron-beam bombardment; supercritical fluid extraction and oxidation; fixed-bed, high-temperature catalytic reactors; and steam gasification. These techniques are not totally effective, they are very often cost-intensive, they are often inconvenient to apply to mixed solid-liquid wastes, and they are not readily adapted to a wide variety of conditions. The application of electrohydraulic cavitation in its various forms for the pyrolytic and oxidative control of hazardous chemicals in water has the poten­ tial to become economically competitive with existing technologies. In terms of convenience and simplicity of operation, electrohydraulic cavitation could 3

2

2

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

12.

235

Collapsing Cavitation Bubbles

KOTRONAROU & HOFFMANN

prove to be far superior to many of the methods listed. For example, the relative efficiency of ultrasound in terms of the total power consumed per mole of p-nitrophenol degraded per liter of water is far superior to U V photolytic degradation. We recently reported (3 ) that ultrasonic irradiation of alkaline oxic aque­ ous solutions of bivalent sulfur, S(-II), at 20 k H z resulted in the rapid oxi­ dation of S(-II). The observed distribution of the oxidation products was sim­ ilar to that reported for 7-radiolysis of S(-II). The ultrasound-induced oxidation of S(-II) in alkaline solutions was attributed to the reaction of H S " with OH* radicals (3). These radicals form during ultrasonic irradiation of water as a result of the high-temperature decomposition of water vapor inside the hot cavitation bubbles (1,2). Although the experimental results were qual­ itatively consistent with our proposed mechanism, some questions remained unanswered concerning the amount of "OH released into the aqueous phase and the existence and relative importance of additional oxidants. To address these questions, a comprehensive aqueous-phase mechanism that describes the free-radical chemistry of the S(-II) + Ό Η + 0 system was developed. This mechanism was subsequently used to model the ultra­ sonic oxidation of S(-II) in alkaline p H . 2

Experimental Approach The free-radical chemistry of the sulfur system is complicated and includes a variety of species and reactions. We developed a mechanism that can accu­ rately model the overall behavior of the S(-II) + Ό Η + 0 system with the minimum number of intermediates. Furthermore, we limited our interest to the neutral-to-alkaline p H region where the ultrasonic irradiation of S (-II) experiments were performed. The chemical species included in the mechanism are as follows: 2

• Nonradical group species: S(-II) = H S + H S S(-I) = H S + H S ~ + S " S(IV) = H S O 3 - + so 3 2 2

2

2

2

2

2

• Nonradical single species: 0 , S 0 ~ , S O / , H 0 , N 0 " , N 0 " 2

2

3

2

-

2

2

2

3

• Radicals: Ό Η , HS', H S " , HSOH*~, S 0 ~ , " S A O H " , * S 0 - , 0 - , SO3-, S 0 - , H S \ H S O , N 0 2

2

4

2

2

2

2

2

e

e

2

4

6

3

2

S(-II), S(-I), and S(IV) are "group species", representing the sum of reactant species in rapid acid-base equilibrium. Equilibrium reactions relevant to our system are shown in Table I. Only the first four reactions are actually used in the mathematical model. The p K values for the reactions of the remaining

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

236

AQUATIC CHEMISTRY

Table I. Equilibrium Reactions Relevant to the S(-II) System Equilibrium H 0(1)

Reaction

H

2

H S ^ H

HSO3- τ± H HS " # H 2

N 0 + O H " 2

2

2

2

2

2

4-

N 0 + "OH — N 0 H 2 N 0 4- S(IV) 4- H 0 — 2 N 0 SO/" + 3H S O / " + S(-II) — S O / " + HS" H S - — HS" + H S 2

3

4-

2

2

+

2

2

+

2

02

44-

44-

S0 HS" SO/" HS S0 HS" — SO/" HS S 0 " 4- 2 0 " — / / — S O / " + S O / HS "OH — HS OH~ H S 4- O H — H S O H S 4- H S O H - — H S 0 4- HS" H S 0 4- 4 " O H —//—> S 0 / 20H4H 2 3

2

3

2

4-

2

2

2

2

A

2

2

4-

2

2

4-

2

4-

X X X X

10 10 10 10

8

7

10

9

1.7 X 10 1.0 X 10 5.3 X 10

9

1.0 X 10

8

7

5FO

1.0 1.0 1.0 1.0 1.0

X X X X X

10 10 10 10 10

8

5

9

9

9

8 9 7 7 16 EST 10 EST EST EST EST EST EST

2

2

+

5.3 2.7 1.0 1.3

1.0 X 10

9

E S T : estimated (see text). Rate constant in reciprocal seconds.

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

EST

238

AQUATIC CHEMISTRY

magnitude as the rate constant for H S ' + HS" (R6); a value of 5.5 Χ 10 M " s" is therefore used. The choice of fc is not critical for our application because H S is not the main S(-II) species at alkaline p H . The rate constant for the reaction of HSOH"~ with 0 ( R l l ) is expected to be of the same order of magnitude as for the reaction of HSOH"~ with HS" (R9) and lower than the rate constants for the reaction of HS* with those species (R7, R6); the value of 10 M " s" is therefore used for R l l . The overall rate of S(-II) oxidation does not seem to be sensitive to fc . At p H 10 and [S(-II)] = 200 μΜ, the kinetics and product distribution remained the same even when k was set to 5 Χ 10 M " s" . Although S 0 " is a known product of the radiolysis of S(-II), no path­ ways that lead to its formation have been proposed. We included two possible pathways: the reaction of H S ~ with S 0 ~ (R14) and oxidation of H S ~ by Ό Η (R44) followed by successive addition and abstraction reactions (R45 and multistep R47). The rate constant of R14 is not expected to be higher than the rate constant for the reaction of S 0 ~ with N 0 (R38) and was therefore set at 10 M " s" . The rate constants for reactions R44-R47 are expected to be near the diffusion-controlled limit and were set at 10 M " s" . Even i f k = 10 M " s and k = 5 Χ 10 M " s" , these reactions cannot account for the observed formation of S 0 ~ . However, the values of these rate con­ stants are not critical for the overall rate of S(-II) oxidation. The rate constant for the reaction of H S ~ with 0 (R15) is expected to be higher than the rate constant for the reaction of H S ~ with S 0 " (R14); a value of 5 Χ 10 M " s" was therefore used for k . Sulfate radical is a very strong oxidant and is expected to react with S(-II) near the diffusion-con­ trolled limit; the value of fc was set at 10 M " s" . Sulfur dioxide and sulfite radicals are expected to react with S (-II) slower than S0 *~, and a value of 10 M " s" was used for k and fc . Reaction R41 should be seen as multistep where the nucleophilic adduct S 0 H S " formed by the reaction of S0 "~ and HS" reacts further with 0 . The model parameters are shown in Table III. The model accepts a con­ stant and continuous input of "OH, H 0 , and N 0 ~ ( O H , H O , and N 0 j , respectively) so that it can simulate the continuous release of those 9

1

1

r5

2

2

9

1

1

rll

0

9

rll

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

2

3

1

1

2

2

3

3

7

1

2

2

2

2

e

1

9

8

rU

1

1

Tii

9

i 7

2

3

1

1

1

1

2

2

2

2

7

1

1

3

2

Tl5

9

r39

1

1

4

8

1

1

r41

r42

2

2

2

2

2

2

2

2

input

2

i n p u t

t

species from the collapsing bubbles during sonication. Provision has been made for reaeration of the solution; an overall oxygen-transfer coefficient [Ki(O )] is used, and the rate of 0 addition to the system is K^O^) · ( [ 0 L - [ 0 J ) , where [ O J is the oxygen saturation concentration at the given temperature and pressure and [0 ] is the actual oxygen concentration in solution. a

2

2

sat

2

The values of the model parameters shown in Table III represent the conditions of our sonication experiments. Their selection is discussed in the next section of this chapter.

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

12.

KOTRONAROU & HOFFMANN

Collapsing Cavitation Bubbles

239

Table I I I . Conditions of Sonication Experiments Fixed Model Parameter

°H 2

3.5 μΜ/min

input

H 0 N0

2

i n p u t

2 i

t

Ki(O ) Τ Ρ H a

P

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

Value

2.0 μΜ/min 1.0 μΜ/min 3.7 Χ I O " s" 4

1

298 Κ 1 atm (101.3 kPa) 10.0

Because activation energies for most of the reactions of Table II were not available, Τ and Ρ are fixed at standard conditions. The p H is also treated as a fixed variable to simulate our buffered sonication experiments. The com­ puter code can be modified to correct the rate constants for different Γ or Ρ (assuming that the necessary thermodynamic data for the reactions of Table II become available), or to treat p H as a variable species (by including H as a 23rd chemical species). Given the initial conditions (concentrations of the 22 chemical species at t = 0), the concentrations of the chemical species with time are found by numerically solving the set of the 22 stiff ordinary differential equations (ODE). A n ordinary differential equation system solver, E P I S O D E (17) is used. The method chosen for the numerical solution of the system includes variable step size, variable-order backward differentiation, and a chord or semistationary Newton method with an internally computed finite difference approximation to the Jacobian equation. +

Model Results and Discussion During ultrasonic irradiation of aqueous solutions, Ό Η radicals are produced from dissociation of water vapor upon collapse of cavitation bubbles. A fraction of these radicals that are initially formed in the gas phase diffuse into solution. Cavitation is a dynamic phenomenon, and the number and location of bursting bubbles at any time cannot be predicted a priori. Nevertheless, the time scale for bubble collapse and rebound is orders of magnitude smaller than the time scale for the macroscopic effects of sonication on chemicals (2) (i.e., nano­ seconds to microseconds versus minutes to hours). Therefore, a simplified approach for modeling the liquid-phase chemistry resulting from sonication of a well-mixed solution is to view the Ό Η input into the aqueous phase as continuous and uniform. The implicit assumption in this approach is that the kinetics of the aqueous-phase chemistry are not controlled by diffusion limi­ tations of the substrates reacting with Ό Η .

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

240

AQUATIC CHEMISTRY

The mathematical model presented here was first used to simulate the oxidation of S(-II) at p H 10, [S(-II)] = 196 μΜ, and [O ] = 240 μΜ (air saturation). These initial conditions correspond to the conditions of one of the sonication experiments conducted in a stainless steel cell at 20 k H z and —75 W / c m with a Branson 200 sonifier and a Vè-inch direct-immersion horn (3). The rates of H 0 and N O input to the system (i.e., H 0 and N 0 , respectively) were set at the experimentally observed zero-order formation rates for those species in deionized water buffered at p H 10 and sonicated under the same conditions. Various runs were performed with different values ofOH , Figure 1 shows the model-calculated evolution of total sulfide with time for six different Ό Η input values. As expected, the initial S(-II) oxidation rate increases with increasing O H . But that initial linear decrease of [S(—II)] is "halted" at [S(—II)] 55 μΜ in all cases. Figure 2 explains why; the main oxidant in our system turns out to be molecular oxygen present in the solution. The ratio of [0 ] :[S(-II)] is about 1.7 in all cases, a result showing that most of the oxygen contained in the oxidized forms of sulfur that are the final products (i.e., S 0 , S 0 ~ , and S 0 ~) comes from 0 and not from Ό Η . Figure 3 shows schematically the reactions and species that proved to be the most significant. The oxidation of S(-II) is initiated by reaction with Ό Η , but is further propagated by a free-radical chain-reaction sequence i n ­ volving 0 . The value of O H that results in an initial rate of S(-II) oxidation equal to the experimentally observed oxidation rate at the stated conditions (i.e., 7.5 0

2

0

2

2

2

a

2

2 i n p u t

2 i n p u t

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

t a p u

input

2

depleted

oxidized

4

2 _

3

2

2

3

2

2

2

i n p u t

Time ( m i n ) Figure I. [S(-II)] profiles for various OH

input

and [O ] 2

0

values; pH 10, [S(-II)]

= 240

0

= 196 μΜ,

μΜ.

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

12.

KOTRONAROU & HOFFMANN

241

Collapsing Cavitation Bubbles

Time ( m i n ) Figure 2. [OJ profiles for various OH

input

and

[OJ = 0

values; pH 10, [S(-II)]

0

240

= 196 μΜ,

μΜ.

μΜ/min at [S(-II)] = 196 μΜ and p H 10) is 3.5 μΜ/min. To explain the experimentally observed linear S(-II) decrease even after all of the initial 0 should have been depleted, it is necessary to assume oxygen transfer from headspace to solution during sonication. Figure 4 shows the calculated [S(-II)] and [0 ] profiles for O H = 3.5 μΜ/min and six different values of the overall oxygen-transfer coefficient K ( 0 ) . The value of Κχ(0 ) does not affect the initial oxidation rate, but it determines the subsequent form of the [S(—II)] curve. If not enough oxygen is added into solution, oxygen is depleted 0

2

2

t a p u t

1

2

2

Figure 3. Main pathways for the S(-II) + OH system in the presence of 0 at alkaline pH. 2

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

242

AQUATIC CHEMISTRY

Time (min) Figure 4. Top: [S(-II)] profiles for different oxygen-transfer coefficients; pH 10, input = μΜ/min, [S(-II)] = 196 μΜ, and [Oj = 240 μΜ. Bottom: Corresponding [OJ profiles. OH

3

5

0

0

before all of the initial sulfide is oxidized, and the result is a sudden decrease in the oxidation rate. If a lot of oxygen is added to the system, [0 ] near the end of the reaction is constantly higher than [S(-II)] and a slowdown of the rate of [S(-II)] oxidation occurs [the intermediate species involved in the chain mechanism will react preferably with 0 and less with S(-II)]. The value of K^Ocj) that results in a continuous linear [S(-II)] decrease is 3.7 Χ 10" per second = 32 per day. Experiments using the same direct-immersion horn that was used in S (-II) sonication, but in a completely different reaction vessel under different 2

2

4

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

12.

KOTRONAROU & HOFFMANN

243

Collapsing C&vitmtion BubUes

Sonication t i m e (min) Figure 5. Comparison between [$(-11)] decrease predicted by the free-radical chemistry model and that observed upon ultrasonic irradiation of S(-II) at pH 10, [S(-II)] = 196 μΜ, and [Oj = 240 μΜ. 0

0

conditions (e.g., higher Τ and open to the atmosphere), gave an oxygen-trans­ fer coefficient that was greater than 32 per day. Therefore, the value of Κ (0 ) was accepted as reasonable and was used in all subsequent modeling work. The value of Κ (0 ) is specific for a particular reactor, because reaeration will depend on the mixing pattern and the ratio of the surface area to the total volume of the solution. Figure 5 compares the experimentally observed [S(—II)] profile (Figure 4 top) with the model results by using the parameter values shown in Table III. In agreement with the experimental results, the values of H 0 and N0 are not critical for the rate of S(-II) oxidation. Therefore, the initially chosen values (i.e., 2.5 and 1.0 μΜ/min, respectively) were not changed. The parameters of Table III were then used to model the oxidation of S(-II) at p H 10 and different initial sulfide concentrations, [S(-II)] . The agreement with the experimental data was very good at low [S(-II)] ; the calculated S(-II) profiles for [S(-II)] = 7 and 45 μΜ are shown in Figure 6, together with the experimental S(-II) profiles. As [S(-II)] increases, oxygen gets depleted before complete oxidation of the initial sulfide is achieved. Ox­ ygen depletion results in a sudden decrease in the overall oxidation rate. Fig­ ure 7 shows the calculated [S(-II)] and [0 ] profiles for [S(-II)] = 300 μΜ and two different values of the oxygen-transfer coefficient; the solid line rep­ resents the case in which [0 ] is fixed at the initial air-saturation value [by providing a very high K ^ O ^ value], and the broken line is expected to rep­ resent our experimental conditions. For that value of [S(-II)] , continuous aeration of the solution does not improve the S (-II) oxidation rate significantly. χ

χ

2

2

2 input

2 i n p u t

0

0

0

0

2

0

2

0

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

2

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

244

AQUATIC CHEMISTRY

Ui

.

0.00

1

0.40

.

,

.

1

0.80

.

1.20

1

•

1

1.60

2.00

Sonication time (min) Figure 6. Comparison between [S(-II)] decrease predicted by the free-radical chemistry model and that observed upon ultrasonic irradiation of S(-II) at pH 10, [OJ = 240 μΜ, and two different [S(-II)] low values: 45 (top) and 7 (bottom) μΜ. 0

0

The same is shown to be true up to [S(-II)] — 450 μΜ (Figure 8). At higher [S(-II)] , the observed S(-II) oxidation rate is lower than the rate at [ 0 ] = constant = 240 μΜ; Figure 9 illustrates that point for [S(-II)] = 955 μΜ. 0

0

2

0

Figure 10 shows the agreement between the experimentally determined effect of [S(-II)] on the initial sulfide oxidation rate, k , for [S(-II)] ^ —450 μΜ. In both cases, k increases linearly with [S(-II)] . The following linear relationship was found from the model: k = 4.4 + 0.016 [S(-II)] , where k is in micromolars per minute and [S(-II)] is in micromolars. The value of the 0

0

0

0

0

0

0

0

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

0

12.

r—,

245

Collapsing Cavitation Bubbles

KOTRONAROU & HOFFMANN

160-

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

80H 40 0

— [08]=240μΜ, constant - - Κ1(θϋ)=3.7Ε-4 s-» 30

20

10

250-

200-

S 1503. 100-

50-

Kl(o )=3.7E4s- \ Kl(o )=3.7E-4s- ^ 1

a

1

a

5

x

—ι—

V0

15 15

j

25

20

30

Sonication time (min) Figure 7. Top: Comparison of calculated [S(-II)] profiles with [OJ kept constant at air saturation (solid line) and with the oxygen-transfer coefficient of Table III (broken line) at pH 10, OH = 3.5 μΜ/min, [S(-II)] = 300 μΜ, and [Oj = 240 μΜ. Bottom: Corresponding [0 ] profiles. input

0

0

2

intercept represents the contribution of ( S D O H , whereas the slope reflects the free-radical chain sequence (3). For [S(-II)] > —300 μΜ, free-radical chain sequence exceeds the contribution of Ό Η (i.e., 0 becomes the prin­ cipal oxidant). 0

2

The two pathways that are used to model S 0 formation cannot outcompete the reaction of H S with 0 . This fact results in an underprediction of [ S 0 ] , as can be seen in Figure 11. Sulfite, on the other hand, is modeled rather well. This situation can also be seen in Figure 12, where the profiles of [S(—II)] and its oxidation products are presented for p H 10.6. Nevertheless, 2

2

2

3

2

3

2 -

2

2_

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

246

AQUATIC CHEMISTRY

^

X

250200-

•—• 1 5 0 -

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

100-

Kl(o )=3.7E4sKl o )=3.7E-4sExperiment 1

2

50-

(

2

t

—

10

15

|

—

25

20

250-

200-

2

150-

6

iooH

50H — --

Kl««=3.7E4sKl(o )=3.7E-4s1

2

5

>

10

\ \ 15

'

20

'

25

30

Sonication time (min) Figure 8. (Top): Comparison of sonolysis data with calculated [S(-II)] profiles, with [OJ kept constant at air saturation (solid line) and with the oxygen-transfer coefficient of Table III (broken line) at pH 10, OH = 3.5 μΜ/min, [S(-II)] - 450 μΜ, and [OJ = 240 μΜ. Bottom: Corresponding calculated [OJ profiles. input

0

0

the free-radical chemistry mechanism adequately describes the overall oxida­ tion of S(-II) upon sonication at alkaline p H . Figures 13, 14, and 15 present the S(-II) and S , where S = [ S O / ] + [ S 0 ] + 2[S 0 ~], profiles observed upon sonication of S(-II) aqueous solutions at p H 9.0, 8.5, and 7.4, respectively. The broken lines represent the corresponding concentrations of those species predicted by the free-radical chemistry mechanism. The free-radical mechanism underpredicts the rate of S(-II) disappearance at p H ^ 8.5. Nevertheless, the total amount of the ox­ idized S(-II) that was found in the form of the three species that form S is ox

3

2_

2

3

-

ox

2

ox

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

12.

Ë

247

Collapsing Cavitation Bubbles

KOTRONAROU & HOFFMANN 1.00

1

0.80-

·

I

'

1

•

0.60-

•

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

0.20-

0.00-

— •

MODEL. Kl(o )=3.7E4sEXPERIMENT

,

^

20

60

40

Sonication time (min) Figure 9. Comparison of sonolysis data with calculated [S(-II)] profiles with [OJ kept constant at air saturation (solid line) at pH 10, OH = 3.5 μΜ/min, [S(-II)] * 955 μΜ, and [O ] = 240 μΜ. input

0

2

0

not much higher than the calculated S . In the chemical model, S represents the total amount of sulfide that has been oxidized because the three species included in S are the only final oxidation products), whereas in the case of the experimental data S represents only a part of the total oxidation products (3). These results provide further evidence that an important pathway for S(-II) sonolysis at p H ^ 8.5 is thermal decomposition of H S within the ox

ox

ox

ox

2

20-

EXPERIMENT] MODEL

15-

β 4.

ο

5H

200

400

S ( - I I ) o (μΜ) Figure 10. Effect of [S(-II)] on initial zero-order S(-II) oxidation rate, 1%. 0

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

248

AQUATIC CHEMISTRY

I

'

'

'

1

α Δ ο •

160-

S0 S0 -* S 0 -* S(-II) 8

4

a

t

a

"

120(0

80-

ο

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

40ο

ο n-4 τ

0

1

·

«

1

10

1

«

'

ο 1—^

20

Χ * • ·

'

1

30

Sonication t i m e (min) Figure 11. [S(-II)] profile and oxidation product distribution at pH 10, and [S(-II)] = 196 μΜ/min. Model results (solid and broken lines) and experimental data (symbols) are shown. 0

cavitation bubbles or within the gas-liquid interface. Furthermore, they seem to suggest that elemental sulfur is the main product of that alternative sonolysis pathway. In conclusion, the sonolysis of S(-II) in the p H range where that species is primarily in the form of HS~ and is not expected to undergo thermal de­ composition can be modeled with an aqueous free-radical chemical meeha-

Sonication time (min) Figure 12. [S(-II)] profile and oxidation product distribution at pH 10.6 and [S(-II)] = 96 μΜ/min. Model results (solid and broken lines) and experimental data (symbols) are shown. 0

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

12.

249

Collapsing Cavitation Bubbles

KOTRONAROU & HOFFMANN 100-

V

S(—Π) EXP MOD

— S(-n) 80-

60H

40-

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

ο ο

20H

r

4

6

8

Sonication time

r~

r

12

10

__

f

1

r

14

(min)

Figure 13. Comparison between [S(-II)] decrease predicted by the free-radical chemistry model and that observed upon ultrasonic irradiation of S(-II) at pH 9.0, [S(-II)] = 91 μΜ, and [Oj = 240 μΜ. 0

0

nism and a continuous constant release of Ό Η into solution. This simplified approach is not valid at the p H range ^8.5 in which a significant part of the total sulfide is in the form of H S , which can participate in the gas-phase, high-temperature chemistry that takes place inside and near collapsing cavi­ tation bubbles. A n extended chemical mechanism that would include both gas- and liquid-phase chemistry is needed to model S(-II) sonolysis in the 2

100

m S(-II) EXP ο Sox EXP — S(-n) MOD - - Sox MOD

80-

3. 60·

40-

ο ο

20-

0-¥·

4

6

8

10

Sonication time

ι

12

r

1

ι

r

14

(min)

Figure 14. Comparison between [S(-II)] decrease predicted by the free-radical chemistry model and that observed upon ultrasonic irradiation of S(-II) at pH 8.5, [S(-II)] = 88 μΜ, and [OJ = 240 μΜ. 0

0

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

250

AQUATIC CHEMISTRY

Sonication time

(min)

Figure 15. Comparison between [S(-II)] decrease predicted by the free-radical chemistry model and that observed upon ultrasonic irradiation of S(-Il) at ρ H 7.4, [S(-II)] ~ 80 μΜ, and [Oj = 240 μΜ. 0

0

general case. However, the development of the next-level model is not feasible at this stage because not enough is known about the number and the size distribution of cavitation bubbles. In addition, little is known about the phys­ ical conditions inside the bubble and its surrounding region upon collapse. Molecular oxygen is important for the sonolysis of S (-II) at alkaline p H because it propagates a free-radical chain reaction that is initiated by " O H . Furthermore, the enhancement of oxygen transfer upon sonication with a direct-immersion horn is considerable. These results may have important i m ­ plications for the application of ultrasonic irradiation for the destruction of chemical contaminants in water systems.

Acknowledgments Many are grateful to German Mills for useful and stimulating discussions, This work was funded in part by U.S. Environmental Protection Agency (Explor­ atory Research Office Grant R815041-01-0) and the Advanced Research Proj­ ects Agency ( D o D - O N R Grant N0014-92-J-1901).

References 1. Riesz, P.; Kondo, T. Free Rad. Biol. Med. 1992, 13, 247. 2. Suslick, K. S. In Ultrasound: Its Chemical, Physical, and Biological Effects; Suslick, K. S., E d . ; VCH: New York, 1988. 3. Kotronarou, Α.; Mills, G.; Hoffmann, M . R. Environ. Sci. Technol. 1992, 25, 2940. 4. Smith, R. M . ; Martell, A. E . Critical Stability Constants; Volume 4: Inorganic Complexes; Plenum, New York, 1976.

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

12. 5. 6. 7. 8. 9.

Downloaded by UNIV OF PITTSBURGH on June 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0244.ch012

10. 11. 12. 13. 14. 15. 16. 17.

KOTRONAROU & HOFFMANN

Collapsing Cavitation Bubbles

251

Hoffmann, M . R. Environ. Sci. Technol. 1977, 11, 61. Giggenbach, W. Inorg. Chem. 1971, 10, 1333. Pandis, S. N . ; Seinfeld, J. H. J. Geophys. Res. 1989, 94, 1105. Neta, P.; Huie, R. E.; Ross, A . B. J. Phys. Chem. Ref. Data 1988, 17, 1027. Buxton, G . V.; Greestock, C . L . ; Helman, W. P.; Ross, A. B. J. Phys. Chem. Ref. Data 1988, 17, 513. Mills, G.; Schmidt, K. H . ; Matheson, M . S.; Meisel, D. J. Am. Chem. Soc. 1987, 91, 1590. Mehnert, R.; Brede, O. Radiat. Phys. Chem. 1984, 23, 463. Chameides, W. L . ; Davis, D. D. J. Geophys. Res. 1982, 87, 4863. Jacob, D. J. J. Geophys. Res. 1986, 91, 9807. Mader, P. M . J. Am. Chem. Soc. 1958, 80, 2634. Hoffmann, M . R.; Edwards, J. O. Inorg. Chem. 1977, 16, 3333. Clifton, C . L . ; Altsein, N.; Huie, R. E . Environ. Sci. Technol. 1988, 22, 586. Byrne, G . D.; Hindmarsh, A. C . ACM Trans. Math. Software 1975, 71.

RECEIVED

for review October 23, 1992.

ACCEPTED

revised manuscript June 11,

Huang et al.; Aquatic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1995.

1993.